Question

Proof delta(t/2) = 2*delta(t)

Where delta: Dirac delta function http://en.wikipedia.org/wiki/Dirac_delta_function

Answer 1

\[\Delta \frac{ t }{ 2 }=2 \Delta\]

Answer 2

take derivative

Answer 3

(1/2) Delta t= (1/2) Delta

Answer 4

Last night I finally got to a decent proof :)

\[\int\limits_{}^{} \delta(t/2) dt \rightarrow \left(\begin{matrix}t/2=\tau \\ dt = 2d \tau \end{matrix}\right) \rightarrow \int\limits_{}^{} 2*\delta(\tau) d \tau\]

And since \[\tau\] is a "dummy variable"

\[\delta(t/2) = 2\delta(t)\]